Papers by Keyword: Finite Deformation

Abstract: This paper deals with an experimental analysis of hard rubber dynamic tests under finite torsion deformations. The experimental test rig was designed and composed for torsion loading of rubber under defined amplitudes, frequencies and temperatures. The present paper brings an amplitude-temperature analysis of isoprene-butadiene rubber ascertained by the use of the test rig. The mathematical rheological model of rubber was designed for phenomenological description and parametric identification of rubber.

Abstract: The Natural Strain suggested in this paper satisfies the additive law of strain on an identical line element in a body. Therefore, it can be defined from anywhere on the basis of the deformed intermediate state. So, this is an effective strain notation to describe the phenomenon that depends on the deformation history such as the plastic deformation. In this paper, the shape of the yield surface generated after applying the pre-deformation of large simple shear is estimated on the basis of the Natural Strain theory. Using the test pieces made of pure copper, which is already subjected to the pre-deformation of large simple shear, the proportional loading tests for combined loading of tension and torsion are carried out beyond the elastic region. The yield stress for each direction in the stress space is determined by investigating the tangent modulus of deviatoric stress- deviatoric strain curve, and the shape of yield surface is elucidated by comparing with the shape by conventional proof stress.

Abstract: For a finite deformation body, there are large strains and displacements on the crack tip. So it is necessary to study-integral based on finite deformation theory. Base forces theory is a new theory for describing finite deformation. In this paper, -integral based on base forces theory are presented. This work provides a new theoretical foundation for studying dynamic crack propagation.

Abstract: The paper is dedicated to applied problems of dynamic stability of deformable systems. Dynamics of boring columns for shallow drilling (up to 500 m) applied in oil-gas extractive industry is considered. The purpose is investigation of influence of the drill rod's material properties of amplitude-frequency characteristic and stability of movement. Deformation of the drill rod is assumed finite. A model of a compressed-torsioned drill rod is considered within the nonlinear theory of finite deformations of V.V. Novozhilov. Dynamic of elastic movement for steel and dural drill rods applied in the extractive industry, resonant vibration modes and instability zone are investigated. The resonant vibrations of drill rods on the basic and higher (third) frequencies and their stability are calculated.

Abstract: Based on the finite deformation theory nonlinear differential equations of uniform-sectional circular arch is deduced, and analytical solution for displacement of the non-hinged arch under load is obtained. This paper provides a theoretical basis for the analysis and calculation of the long span arch.

Abstract: The purpose of the paper is modeling of nonlinear vibrations and stability of movement of boring columns at finite deformations. Movement of boring columns for shallow drilling (up to 500 m) applied in oil-gas extractive industry is considered. Nonlinear models of movement of acompressed-torsioned drill rod within the nonlinear theory of finite deformations of V.V. Novozhilov are constructed. A method for its analysis and criterion of dynamic stability are offered. The numerical analysis of its elastic dislocations and instability zones of the basic resonance is carried out, which confirm the efficiency of the offered nonlinear dynamic model of rod elements and techniques for their calculation.

Abstract: Object Stress rates to predict the behavior of material have been researched based on numerically and theoretically for researchers who study continuum mechanics due to its complexity. This study focused on the various objective stress rates which assumed the finite deformation theory. Eight object stress rates (Oldroyd, Truesdell, Cotter–Rivlin, Jaumann, Green–Naghdi, Eulerian, grangian, and logarithmic object stress rates) were introduced using continuum mechanics and analyzed to derive the numerical solution to the simple shear problem. Numerical results from each object stress rate were analyzed and compared with the results of the other stress rates. Finally, the appropriate object stress rate for the simple shear problem was determined based on the numerical results from eight objects stress rates.

Abstract: A new constitutive model which is modified from Gao’s constitutive model has been introduced to analyze the finite deformation of a circular membrane with an embedded rigid inclusion under uniform pressure. Based on the basic controlling equations, the constitutive parameters and the dimension of the rigid inclusion have been discussed to demonstrate the influences on the membrane stresses.

Abstract: In general, there are large strains and displacements on the crack tip. So it is necessary to study-integral and its dual form based on finite deformation theory. Base forces theory is a new theory for describing finite deformation. -integral and its dual form based on base forces theory are presented in the paper. This work provides theoretical foundation for studying crack propagation.

Abstract: This paper analyses the mechanical behavior of matrix material and cell structure of closed-cell foam rubber by Gibson-Ashby model and the strain energy function of incompressible rubber-like material. The constitutive relation of closed-cell foam rubber is established by the overlay analysis of the two impact factors. The constitutive data for the new model is fitted and the uniaxial compression experiment is utilized to prove the feasibility of the constitutive equation produced in this paper. The model is in good agreement with the experimental results.